Pre-Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice)
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You can use the sum and difference formulas for cosine to prove trig identities. When working with sum and difference formulas for cosines, you're simply plugging in given values for variables. Just make sure you use the correct formula based on the information you're given in the question.

Here are the sum and difference formulas for cosines:

image0.png

For example, to prove

image1.png

follow these steps:

  1. Outline the given information.

    You start with

    image2.png
  2. Look for sum and/or difference identities for cosine.

    In this case, the left side of the equation is the difference formula for cosine. Therefore, you can break up the first term by using the difference formula for cosines:

    image3.png
  3. Refer to the unit circle and substitute all the information you know.

    The whole unit circle
    The whole unit circle

    Using the unit circle, the equation simplifies to

    image5.png

    which equals sin x on the left-hand side. Your equation now says sin x = sin x. Ta-dah!

About This Article

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About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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